Among the most fundamental questions in the manipulation of quantum resources
such as entanglement is the possibility of reversibly transforming all resource
states. The most important consequence of this would be the identification of a
unique entropic resource measure that exactly quantifies the limits of
achievable transformation rates. Remarkably, previous results claimed that such
asymptotic reversibility holds true in very general settings; however, recently
those findings have been found to be incomplete, casting doubt on the
conjecture. Here we show that it is indeed possible to reversibly interconvert
all states in general quantum resource theories, as long as one allows
protocols that may only succeed probabilistically. Although such
transformations have some chance of failure, we show that their success
probability can be ensured to be bounded away from zero, even in the asymptotic
limit of infinitely many manipulated copies. As in previously conjectured
approaches, the achievability here is realised through operations that are
asymptotically resource non-generating. Our methods are based on connecting the
transformation rates under probabilistic protocols with strong converse rates
for deterministic transformations. We strengthen this connection into an exact
equivalence in the case of entanglement distillation.Comment: 6+10 page